Matching bias in syllogistic reasoning: Evidence for a dual-process account from response times and confidence ratings

We examined matching bias in syllogistic reasoning by analysing response times, confidence ratings, and individual differences. Roberts’ (2005) “negations paradigm” was used to generate conflict between the surface features of problems and the logical status of conclusions. The experiment replicated matching bias effects in conclusion evaluation (Stupple & Waterhouse, 2009), revealing increased processing times for matching/logic “conflict problems”. Results paralleled chronometric evidence from the belief bias paradigm indicating that logic/belief conflict problems take longer to process than non-conflict problems (Stupple, Ball, Evans, & Kamal-Smith, 2011). Individuals’ response times for conflict problems also showed patterns of association with the degree of overall normative responding. Acceptance rates, response times, metacognitive confidence judgements, and individual differences all converged in supporting dual-process theory. This is noteworthy because dual-process predictions about heuristic/analytic conflict in syllogistic reasoning generalised from the belief bias paradigm to a situation where matching features of conclusions, rather than beliefs, were set in opposition to logic.     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

The contribution of logical reasoning to the learning of mathematics in primary school

It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6‐year‐old children's logical abilities and their working memory predict mathematical achievement 16 months later; and (b) logical scores continued to predict mathematical levels after controls for working memory, whereas working memory scores failed to predict the same measure after controls for differences in logical ability. In our second study, we trained a group of children in logical reasoning and found that they made more progress in mathematics than a control group who were not given this training. These studies establish a causal link between logical reasoning and mathematical learning. Much of children's mathematical knowledge is based on their understanding of its underlying logic.     

条件推理:“演绎”与“概率”两种实验研究范式之比较

本研究通过推理心理学研究中的“演绎”和“概率”两种实验范式设计对同一个班级的大学生参与者(实验一中N=57,实验二中N=43)进行先后两次有关条件推理的实验研究后,得出如下主要结果:(1)推理者在对不同的“纯形式条件命题本身的认可度”以及对由它们各自建构的同类型推理题的推理结果之间的作答反应模式之间的差异都很小且具有较高的一致性;(2)对由不同的“含具体内容的假言命题”本身的认可度之间以及由它们建构的同类型条件推理题的推理结果之间具有较大的差异性;(3)推理者对“演绎”和“概率”两种不同实验范式分别建构的内容近似的推进题进行推理时具有大致相同的作答反应趋势。由此可以推论推理者在“概率推理实验范式”中的作答或推理结果可以被视为只是对“演绎推理实验范式”的相应推理题给出“概率解”的心理加工过程。     

Recognition of proofs in conditional reasoning

Relatively little is known about those who consistently produce the valid response to Modus Tollens (MT) problems. In two studies, people who responded correctly to MT problems indicated how “convinced” they were by proofs of conditional reasoning conclusions. The first experiment showed that MT competent reasoners found accurate proofs of MT reasoning more convincing than similar “proofs” of invalid reasoning. Similarly, there was a tendency for MT competent reasoners to find an initial counterfactual supposition more convincing than did people who were less competent in MT. The second experiment showed that when individuals produced the correct MT response, and found correct MT proofs to be more convincing than “bogus” proofs, they were also less likely to find the conclusions to Denying the Antecedent, or Affirming the Consequent problems valid, compared to individuals who could not discriminate between valid and bogus MT proofs. These findings are discussed in terms of both their implications for the mental logic and mental models positions, and individual differences in System 1 and System 2 reasoning.     

Braine心理逻辑理论述评

该文对Braine提出的在推理心理学研究领域占居重要地位的“心理逻辑理论”做了综合述评。“心理逻辑理论”主要包括三方面内容:构成“心理逻辑理论”基础的一组推理规则图式、将推理规则图式应用于推理过程的推理方案、实际应用意义。Braine认为他和他的同事于1984年设计并实施的以“自然推理系统”所含各推理规则为实验材料的实验结果支持该理论的基本观点。     

Rips的“证明心理学理论”述评

该文对Rips提出的“证明心理学理论”做了综合述评。这一理论主要包含三方面的内容:对推理过程与人类记忆相互关系的解释;(2)根据逻辑学中的“自然推理规则”进行修正后用于解释人类推理过程的推理规则;(3)关于如何控制推理过程的论述。Rips认为他于1983年设计并实施的以“自然推理系统”所含各推理规则为实验材料的实验结果支持该理论的基本观点。     

Deductive reasoning and matching-bias inhibition training: Evidence from a debiasing paradigm

Using the matching bias example, the aim of the present studies was to show that adults' reasoning biases are due to faulty executive inhibition programming. In the first study, the subjects were trained on Wason's classical card selection task; half were given training in how to inhibit the perceptual matching bias (experimental group) and half in logic without the inhibition component (control group). On the pre- and post-tests, their performance was assessed on the Evans conditional rule falsification task (with a negation in the antecedent of the rule), a task that also involves matching bias. In addition, subjects were tested for perceptual field dependence/independence using the Embedded Figures Test. The results brought out a specific inhibition training effect, as well as a clear-cut relationship in the experimental group between receptiveness to training and perceptual field independence. In the second study, the training paradigm was the same except that on the pre- and post-tests, the negation was in the consequent of the conditional rule (in this case, the perceptual matching response corresponds to the logical response). The subjects succeeded on the pre-test, and the matching-bias inhibition training had a negative effect on post-test performance. This specific negative priming effect confirms the inhibitory impact of our experimental training and outlines the dissociation of inhibition and logical components.     

Belief–logic conflict resolution in syllogistic reasoning: Inspection-time evidence for a parallel-process model

An experiment is reported examining dual-process models of belief bias in syllogistic reasoning using a problem complexity manipulation and an inspection-time method to monitor processing latencies for premises and conclusions. Endorsement rates indicated increased belief bias on complex problems, a finding that runs counter to the “belief-first” selective scrutiny model, but which is consistent with other theories, including “reasoning-first” and “parallel-process” models. Inspection-time data revealed a number of effects that, again, arbitrated against the selective scrutiny model. The most striking inspection-time result was an interaction between logic and belief on premise-processing times, whereby belief – logic conflict problems promoted increased latencies relative to non-conflict problems. This finding challenges belief-first and reasoning-first models, but is directly predicted by parallel-process models, which assume that the outputs of simultaneous heuristic and analytic processing streams lead to an awareness of belief – logic conflicts than then require time-consuming resolution.     

广义论证视域下朱熹论辩逻辑体系的考察

近年来,广义论证视域下的中国古代逻辑史研究成为学界关注的热点,在丰硕的研究成果中,仍存在“怎样深化”与“如何拓展”等问题。在广义论证视域下对朱熹论辩逻辑体系进行考察,一方面可以打破以往研究主要集中在先秦时期的囿限,进一步拓展其研究范围;另一方面也可以在逻辑体系的构建中深化中国古代逻辑研究。从广义论证角度看,朱熹的逻辑是“名义界分”“知言穷理”等说理论证规则的集合,基于上述逻辑,朱熹同陆九渊、张栻等人围绕“太极”“仁说”等进行论辩实践,逐步建立起以名、辞理论为基础的“名、辞–辩”的逻辑体系。上述体系对后世影响深远。从广义论证角度考察朱熹论辩逻辑体系,对新时期回应如何做“中国古代逻辑”具有启发意义。     

Wittgenstein and logical necessity

An attempt is made to show that Wittgenstein's later philosophy of logic is not the kind of conventionalism which is often ascribed to him. On the contrary, Wittgenstein gives expression to a “mixed” theory which is not only interesting but tends to resolve the perplexities usually associated with the question of the a priori character of logical truth. I try to show that Wittgenstein is better understood not as denying that there are such things as “logical rules” nor as denying that the results of applying such rules are “logically necessary,” but as trying to understand what it is to appeal to a logical rule and what it means to say that the results of applying such a rule are “necessary.” He is not so much overthrowing standard accounts of logical necessity as discovering the limits of the concept.     

Persisting Effects of Instruction on Young Children's Syllogistic Reasoning with Incongruent and Abstract Premises

Studies of reasoning have often invoked a distinction between a natural or ordinary consideration of the premises, in which they are interpreted, and even distorted, in the light of empirical knowledge, and an analytic or logical consideration of the premises, in which they are analysed in a literal fashion for their logical implications. Two or three years of schooling have been seen as critical for the spontaneous use of analytic reasoning. In two experiments, however, 4-year-olds who were given brief instructions that prompted use of an analytic approach continued to adopt this approach one week later. Thus, when given syllogistic problems in which the major premise was incongruent with their empirical knowledge (e.g. “All snow is black”), instructed children reasoned more accurately from that premise both immediately and a week later as compared to children given only a basic introduction. A third experiment showed that instructions also improved 4-year-olds' performance on hard-to-imagine, abstract material (e.g. “All mib is white”). Similarities between the effects of brief instruction and of schooling are discussed.     

A logic for diffusion in social networks

This paper introduces a general logical framework for reasoning about diffusion processes within social networks. The new “Logic for Diffusion in Social Networks” is a dynamic extension of standard hybrid logic, allowing to model complex phenomena involving several properties of agents. We provide a complete axiomatization and a terminating and complete tableau system for this logic and show how to apply the framework to diffusion phenomena documented in social networks analysis.     

Deductive schemas with uncertain premises using qualitative probability expressions

The new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical expressions (e.g., “the chances are high”) and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that (1) except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, (2) the rate of conjunction fallacy was consistently low (not exceeding 20%, even with sure premises), and (3) participants' interpretation of the conditional agreed with de Finetti's “conditional event” but not with the material conditional.     

Effects of order of presentation on conditional reasoning

ABSTRACT

The main goal of this research is to study whether or not the order of presentation of the premises in a logical argument form, such as a conditional reasoning task, could affect the processing time of premises and conclusion and the conclusions that participants accept as valid in an evaluation task. One experiment is reported in which participants are asked to evaluate computer-presented conditionals. Half of the problems were presented in traditional order (“if p then q, p, therefore q”) and half in inverse order (“p, if p then q, therefore q”). The experiment showed that there was an order effect in processing the premises and conclusion: participants took longer to read the premises in traditional order than in inverse order, but they took longer to read the conclusion in inverse order than in traditional order. The finding is discussed with respect to the main theories of conditional reasoning.     

Heidegger: The Role of Logic in his Thought

Since his inaugural lecture at Freiburg in 1929 in which Heidegger delivered his most celebrated salvo against logic, he has frequently been portrayed as an anti-logician, a classic example of the obscurity resultant upon a rejection of the discipline of logic, a champion of the irrational, and a variety of similar things. Because many of Heidegger's statements on logic are polemical in tone, there has been no little misundersanding of his position in regard to logic, and a great deal of distortion of it. All too frequently the position which is attacked as Heidegger's is a barely recognizable caricature of it. We shall, therefore, attempt to determine precisely what Heidegger understands by logic. When he “attacks” logic, as he did in the inaugural lecture, as well as in many other of his writings, what “logic” is he attacking? The word “logic” is, after all, placed in quotation marks which would seem to indicate some special sense. This paper will argue that if one takes logic as it has traditionally been understood and practiced that one is forced to the conclusion that it is incompatible with Heidegger's “way of thought” (Denkweg). This rejection of logic, however, does not deliver him up to irrationalism or the enthronement of blind instinct in place of reason, as some of his critics have charged. Neither is it a self-indulgent refusal to achieve clarity and precision which ends in a kind of mystical pseudo-poetry. Rather, it will be argued, it represents a quite valid, and indeed rich, approach to Being, though certainly not a “logical” one in the traditional sense.     

Dangerous liaisons

In this paper I take side on externalist incompatibilism. However, I intend to radicalize the position. First, based on my criticism of Burge's anaphoric proposal, I argue that there is no reasoning‐transparency: the reasoner is blind to the reasoning he is performing. Second, assuming a global form of content‐externalism, I argue that “in the head” are only logical and formal abilities. That is what I call “bite the bullet and swallow it too.”     

Message Design Logic and Message Goal Structure Effects on Perceptions of Message Quality in Regulative Communication Situations

O'Keefe has suggested that variations in the goal sets individuals choose to pursue and the form of reasoning they employ are sources of variation in message designs. She offered an analysis of the specific consequences of differences in goals (“message goal structure”) and in forms of reasoning (“message design logics”), and shouted how this analysis could be used to describe systematically functional variations in regulative messages. The study reported in this article explored the consequences of differences in message design logic and goal structures for success in regulative communication situations; Messages that differed in these properties were presented to subjects for evaluation on a number of functionally significant dimensions. Level of message design logic was straightforwardly associated with every type of effectiveness that was assessed. Differences in message goal structures had more selective effects on message evaluations, often involving interactions with the level of construct differentiation of the message evaluator.